Meter Scale Plasma Source For Plasma Wakefield ... - CiteSeerX
Meter Scale Plasma Source For Plasma Wakefield Experiments N. Vafaei-Najafabadia, J. L. Shawa, K. A. Marsha, C. Joshia, and M. J. Hoganb a
Department of Electrical Engineering, University of California Los Angeles, Los Angeles , CA 90095 b SLAC National Accelerator Laboratory, Menlo Park, CA 94025
Abstract. High accelerating gradients generated by a high density electron beam moving through plasma has been used to double the energy of the SLAC electron beam [1]. During that experiment, the electron current density was high enough to generate its own plasma without significant head erosion. In the newly commissioned FACET facility at SLAC, the peak current will be lower and without pre-ionization, head erosion will be a significant challenge for the planned experiments. In this work we report on our design of a meter scale plasma source for these experiments to effectively avoid the problem of head erosion. The plasma source is based on a homogeneous metal vapor gas column that is generated in a heat pipe oven [2]. A lithium oven over 30 cm long at densities over 1017 cm-3 has been constructed and tested at UCLA. The plasma is then generated by coupling a 10 TW short pulse Ti:Sapphire laser into the gas column using an axicon lens setup. The Bessel profile of the axicon setup creates a region of high intensity that can stretch over the full length of the gas column with approximately constant diameter. In this region of high intensity, the alkali metal vapor is ionized through multi-photon ionization process. In this manner, a fully ionized meter scale plasma of uniform density can be formed. Methods for controlling the plasma diameter and length will also be discussed. Keywords: Pre-ionized plasma, lithium, axicon, heat pipe oven, plasma wakefield accelerator. PACS: 52.50.Jm
INTRODUCTION A meter scale pre-ionized plasma source is needed for several beam driven plasma wakefield experiments. In electron driven experiments, such as the one at FACET, part of the SLAC National Accelerator Laboratory, the beam has to interact with self-ionized plasma in the absence of pre-ionization. In a self-ionized plasma, as the beam propagates, the ionization front moves backwards in the beam frame as the electrons at the head of the beam expand and lose the ability to further ionize. The rate of this head erosion [1] is proportional to emittance, 1/γ, 1/N1.5, and IP1.73 where γ is the relativistic Lorentz factor of the beam, N is the number of particles in the bunch, and IP is the ionization potential of the material ionized by the bunch. Head erosion is a particularly important limit in two bunch experiments which consist of a trailer beam as well as a driver bunch, where the goal is to accelerate the trailer bunch using the wake created by the driver bunch. The two bunches are created from the same initial beam since they need to fit inside a single plasma period. At FACET, this is done using a notch collimator in combination with dispersive elements [3]. The consequent reduction in the driver charge from one bunch to two bunches is 1.8x1010 to 6-9x109 which makes the head erosion problem significantly worse. Given the design parameters of FACET (see [3]) the head erosion distance in lithium and rubidium vapor sources (to be discussed in next section) will only be 20 and 30 cm respectively. In contrast, 1-2 meters of travel distance in plasma is needed to double the energy of the trailing bunch in the wake of the driver. A pre-ionized plasma would significantly reduce the head erosion of the driver, enabling the energy doubling experiment. Proton driven experiments suffer from a similar problem. The main difficulty with high energy proton beams is that the beam density is too low for the beam to generate the plasma. The pre-ionized plasma source would enable the study of self-modulation of proton beams decoupled from ionization effects, which are of interest to experiments at SLAC and CERN [4]. The plasma source proposed in this paper will be created by laser ionization of an alkali metal vapor. The rest of the paper is thus organized: The next section describes the heat pipe oven used to create the alkali vapor targets. The ionization mechanisms considered are discussed next, and finally the ionization apparatus will be described.
ALKALI METAL HEAT PIPE OVEN The plasma source is an ionized alkali vapor in a heat pipe oven [2]. This device, schematically shown in Figure 1, is used for its ability to create long vapor columns with uniform density profile.
FIGURE 1. Schematics of lithium heat pipe oven (top) and the corresponding pressure (density) profile (bottom)
The operation of the heat pipe oven is as follows: The heater melts the alkali metal (e.g. lithium), creating a vapor pressure that pushes out the buffer gas (helium in the case of the lithium oven) from the central region of the oven. The vapor condenses in the helium-lithium boundary region and is then transferred back to the hot center of the oven by the wick. The water in cooling jackets on either side serves to keep the temperature of the helium low. The pressure of the lithium vapor in the central region is equal to the pressure of the helium. This pressure in turn determines the temperature of the vapor through [5]
Pv ( Li ) =
exp(− 2.0532 ln(T ) − 19.4268 / T + 9.4993 + 0.753 × T ) 133 ×10 6
(1)
Where T is the temperature in kilo Kelvin and Pv is the pressure in Torr. A similar equation for other alkali vapors can be found in [5]. The high thermal conductivity of the alkali vapor ensures that the temperature of the oven is uniform in the central region, which results in a uniform density. With temperature and pressure determined, the density is calculated using the ideal gas law. Figure 2 shows experimental measurement of the temperature profile of a lithium oven (on the left) and the corresponding density profile (on the right). Since the temperature (and density) of the lithium is controlled by the pressure of helium, the heater power can be used to control the length of the oven, in case of Figure 2 creating a density profile that has a FWHM of 32 cm.
FIGURE 2. Experimental temperature (left) and density (right) profiles for a lithium heat pipe oven operating at 912 C with helium buffer pressure at 12.7 Torr, corresponding to lithium density of 1x1017 cm-3.
IONIZATION MECHANISM Tunnel ionization and multiphoton ionization (MPI) are the two mechanisms that apply in the regime of laser powers of interest. In the tunnel ionization regime, the electric field of the laser modifies the potential well of the atom and the electron tunnels through the modified barrier. The equation for the tunnel ionization rate is [6] 2n−1
4 n ξ (eV ) $ ξ 3/2 (eV ) ' W (s ) = 1.5 ×10 &20.5 ) nΓ(2n) % E(GV / m) ( −1
15
$ ξ 3/2 (eV ) ' exp &−6.83 ). E(GV / m) ( %
(2)
Where ξ is the ionization potential, E is the electric field, Γ is the mathematical Gamma function, and n≈3.69Z/ξ1/2 is the effective principle quantum number with Z being the state of ionization; equal to one for a singly ionized atom. Equation (2) shows that the tunnel ionization rate only depends on the electric field and the ionization potential and is independent of the wavelength. In multiphoton ionization, the photon density is so high that multiple photons are absorbed by the same atom simultaneously. The ionization rate for k photon ionization is given by
W ( s −1 ) = σ k F k .
(3)
Where F=I/(hυ) is the photon flux (in units of s-1cm-2) with I being the intensity of the laser and υ the frequency. σk (in units of cm2ksk-1) is the multiphoton ionization cross section and depends on the material and the operating wavelength. As there is significant discrepancy in the reported theoretical values of σk, this parameter needs to be experimentally verified. From the ionization rate, the electron density can be found using
dn = −Wn. dt
(
)
n = n0 exp − ∫ Wdt .
(4)
ne = n0 − n. Where n0 is the initial neutral density, n is the remaining neutral density and ne is the electron density. Ionization intensity threshold is then calculated by carrying out the integration in Equation (4) numerically over the pulse shape, seeking the intensity that results in ne≈n0. Table (1) summarizes the ionization conditions for alkali vapors of interest (Li and Rb) along with three other gases for comparison. The multiphoton ionization threshold for lithium has been taken from the lowest of the experimental values from [7]. An 800 nm laser pulse with 50 fs FWHM has been assumed to calculate the other ionization thresholds. The three-photon cross section for rubidium is obtained from [8]. In addition to the required intensity, the energy required to ionize a satisfactory volume of gas (1 m long cylinder of 1 mm in diameter, with the density of 5x1016 cm-3) is also stated for each element. TABLE (1). Summary of laser ionization requirements. Tunnel ionization thresholds are calculated based on a 50 fs laser pulse. Required laser energy to generate a cold plasma of 1 mm in diameter and 1 m long, with the density of 5x1016 cm-3 IP (eV) Ionization Threshold Energy Ionization Element (Tunnel) Requirement (mJ) Threshold (MPI) 4.17 2.6x1012 Wcm-2 26 4.2x1011 Wcm-2 Rb 12 -2 5.39 7x10 Wcm 34 4x1011 Wcm-2 Li 14 -2 13.6 1x10 Wcm 85 -H2 15.6 1.5x1014 Wcm-2 98 -Ar 24.6 1.4 x1015 Wcm-2 155 -He
As the table shows, the dominant process for ionization of alkali vapors with IP
Department of Electrical Engineering, University of California Los Angeles, Los Angeles , CA 90095 b SLAC National Accelerator Laboratory, Menlo Park, CA 94025
Abstract. High accelerating gradients generated by a high density electron beam moving through plasma has been used to double the energy of the SLAC electron beam [1]. During that experiment, the electron current density was high enough to generate its own plasma without significant head erosion. In the newly commissioned FACET facility at SLAC, the peak current will be lower and without pre-ionization, head erosion will be a significant challenge for the planned experiments. In this work we report on our design of a meter scale plasma source for these experiments to effectively avoid the problem of head erosion. The plasma source is based on a homogeneous metal vapor gas column that is generated in a heat pipe oven [2]. A lithium oven over 30 cm long at densities over 1017 cm-3 has been constructed and tested at UCLA. The plasma is then generated by coupling a 10 TW short pulse Ti:Sapphire laser into the gas column using an axicon lens setup. The Bessel profile of the axicon setup creates a region of high intensity that can stretch over the full length of the gas column with approximately constant diameter. In this region of high intensity, the alkali metal vapor is ionized through multi-photon ionization process. In this manner, a fully ionized meter scale plasma of uniform density can be formed. Methods for controlling the plasma diameter and length will also be discussed. Keywords: Pre-ionized plasma, lithium, axicon, heat pipe oven, plasma wakefield accelerator. PACS: 52.50.Jm
INTRODUCTION A meter scale pre-ionized plasma source is needed for several beam driven plasma wakefield experiments. In electron driven experiments, such as the one at FACET, part of the SLAC National Accelerator Laboratory, the beam has to interact with self-ionized plasma in the absence of pre-ionization. In a self-ionized plasma, as the beam propagates, the ionization front moves backwards in the beam frame as the electrons at the head of the beam expand and lose the ability to further ionize. The rate of this head erosion [1] is proportional to emittance, 1/γ, 1/N1.5, and IP1.73 where γ is the relativistic Lorentz factor of the beam, N is the number of particles in the bunch, and IP is the ionization potential of the material ionized by the bunch. Head erosion is a particularly important limit in two bunch experiments which consist of a trailer beam as well as a driver bunch, where the goal is to accelerate the trailer bunch using the wake created by the driver bunch. The two bunches are created from the same initial beam since they need to fit inside a single plasma period. At FACET, this is done using a notch collimator in combination with dispersive elements [3]. The consequent reduction in the driver charge from one bunch to two bunches is 1.8x1010 to 6-9x109 which makes the head erosion problem significantly worse. Given the design parameters of FACET (see [3]) the head erosion distance in lithium and rubidium vapor sources (to be discussed in next section) will only be 20 and 30 cm respectively. In contrast, 1-2 meters of travel distance in plasma is needed to double the energy of the trailing bunch in the wake of the driver. A pre-ionized plasma would significantly reduce the head erosion of the driver, enabling the energy doubling experiment. Proton driven experiments suffer from a similar problem. The main difficulty with high energy proton beams is that the beam density is too low for the beam to generate the plasma. The pre-ionized plasma source would enable the study of self-modulation of proton beams decoupled from ionization effects, which are of interest to experiments at SLAC and CERN [4]. The plasma source proposed in this paper will be created by laser ionization of an alkali metal vapor. The rest of the paper is thus organized: The next section describes the heat pipe oven used to create the alkali vapor targets. The ionization mechanisms considered are discussed next, and finally the ionization apparatus will be described.
ALKALI METAL HEAT PIPE OVEN The plasma source is an ionized alkali vapor in a heat pipe oven [2]. This device, schematically shown in Figure 1, is used for its ability to create long vapor columns with uniform density profile.
FIGURE 1. Schematics of lithium heat pipe oven (top) and the corresponding pressure (density) profile (bottom)
The operation of the heat pipe oven is as follows: The heater melts the alkali metal (e.g. lithium), creating a vapor pressure that pushes out the buffer gas (helium in the case of the lithium oven) from the central region of the oven. The vapor condenses in the helium-lithium boundary region and is then transferred back to the hot center of the oven by the wick. The water in cooling jackets on either side serves to keep the temperature of the helium low. The pressure of the lithium vapor in the central region is equal to the pressure of the helium. This pressure in turn determines the temperature of the vapor through [5]
Pv ( Li ) =
exp(− 2.0532 ln(T ) − 19.4268 / T + 9.4993 + 0.753 × T ) 133 ×10 6
(1)
Where T is the temperature in kilo Kelvin and Pv is the pressure in Torr. A similar equation for other alkali vapors can be found in [5]. The high thermal conductivity of the alkali vapor ensures that the temperature of the oven is uniform in the central region, which results in a uniform density. With temperature and pressure determined, the density is calculated using the ideal gas law. Figure 2 shows experimental measurement of the temperature profile of a lithium oven (on the left) and the corresponding density profile (on the right). Since the temperature (and density) of the lithium is controlled by the pressure of helium, the heater power can be used to control the length of the oven, in case of Figure 2 creating a density profile that has a FWHM of 32 cm.
FIGURE 2. Experimental temperature (left) and density (right) profiles for a lithium heat pipe oven operating at 912 C with helium buffer pressure at 12.7 Torr, corresponding to lithium density of 1x1017 cm-3.
IONIZATION MECHANISM Tunnel ionization and multiphoton ionization (MPI) are the two mechanisms that apply in the regime of laser powers of interest. In the tunnel ionization regime, the electric field of the laser modifies the potential well of the atom and the electron tunnels through the modified barrier. The equation for the tunnel ionization rate is [6] 2n−1
4 n ξ (eV ) $ ξ 3/2 (eV ) ' W (s ) = 1.5 ×10 &20.5 ) nΓ(2n) % E(GV / m) ( −1
15
$ ξ 3/2 (eV ) ' exp &−6.83 ). E(GV / m) ( %
(2)
Where ξ is the ionization potential, E is the electric field, Γ is the mathematical Gamma function, and n≈3.69Z/ξ1/2 is the effective principle quantum number with Z being the state of ionization; equal to one for a singly ionized atom. Equation (2) shows that the tunnel ionization rate only depends on the electric field and the ionization potential and is independent of the wavelength. In multiphoton ionization, the photon density is so high that multiple photons are absorbed by the same atom simultaneously. The ionization rate for k photon ionization is given by
W ( s −1 ) = σ k F k .
(3)
Where F=I/(hυ) is the photon flux (in units of s-1cm-2) with I being the intensity of the laser and υ the frequency. σk (in units of cm2ksk-1) is the multiphoton ionization cross section and depends on the material and the operating wavelength. As there is significant discrepancy in the reported theoretical values of σk, this parameter needs to be experimentally verified. From the ionization rate, the electron density can be found using
dn = −Wn. dt
(
)
n = n0 exp − ∫ Wdt .
(4)
ne = n0 − n. Where n0 is the initial neutral density, n is the remaining neutral density and ne is the electron density. Ionization intensity threshold is then calculated by carrying out the integration in Equation (4) numerically over the pulse shape, seeking the intensity that results in ne≈n0. Table (1) summarizes the ionization conditions for alkali vapors of interest (Li and Rb) along with three other gases for comparison. The multiphoton ionization threshold for lithium has been taken from the lowest of the experimental values from [7]. An 800 nm laser pulse with 50 fs FWHM has been assumed to calculate the other ionization thresholds. The three-photon cross section for rubidium is obtained from [8]. In addition to the required intensity, the energy required to ionize a satisfactory volume of gas (1 m long cylinder of 1 mm in diameter, with the density of 5x1016 cm-3) is also stated for each element. TABLE (1). Summary of laser ionization requirements. Tunnel ionization thresholds are calculated based on a 50 fs laser pulse. Required laser energy to generate a cold plasma of 1 mm in diameter and 1 m long, with the density of 5x1016 cm-3 IP (eV) Ionization Threshold Energy Ionization Element (Tunnel) Requirement (mJ) Threshold (MPI) 4.17 2.6x1012 Wcm-2 26 4.2x1011 Wcm-2 Rb 12 -2 5.39 7x10 Wcm 34 4x1011 Wcm-2 Li 14 -2 13.6 1x10 Wcm 85 -H2 15.6 1.5x1014 Wcm-2 98 -Ar 24.6 1.4 x1015 Wcm-2 155 -He
As the table shows, the dominant process for ionization of alkali vapors with IP
